Abstract
We study collective synchronization in a large number of coupled
oscillators on various complex networks. In particular, we pay
attention to the relaxation dynamics of synchronization, which is
important in the point of view of information transfer or the
system recovery dynamics from the perturbation. We measure the
relaxation time which takes to establish global synchronization,
varying the structural properties of the networks. It is found
that the relaxation time in the strong coupling regime ($K>K_c$)
exhibits a logarithmic increasing with the network size ($\tau
N$), which is attributed to the initial random phase
given by $1/N$. Under the removal of initial-phase
fluctuation, the relaxation time is found to be independent of the
system size, which implies that the local interaction is
irrelevant in the relaxation dynamics of the synchronization in
the strong coupling regime. The collapsing form of the relaxation
dynamics is also derived, and it shows a good consistency with the
numerical simulations. As an application, we explore the recovery
dynamics of the oscillators when the perturbation comes into the
system.
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